Marcelo Bielsa's Whites failed to muster a single short on target in the whole game in which they had just three attempts at goal.
The Saints bagged the only goal of the game in the 53rd minute when Armando Borja slammed home a fierce finish from the middle of the box to finish a rapid Southampton corner.
The defeat, United's fourth loss of the Premier League season, left the Whites fourth bottom.
Graham Smyth, the YEP's chief football writer, hands out the scores from an afternoon to forget at St Mary's.
7. Jamie Shackleton
5 - Some bright moments in possession in the second half. Kept fighting to the end. Photo by GLYN KIRK/AFP via Getty Images.
8. Dan James
4 - His pace caused problems or gave Leeds an outlet on rare occasions. End product was lacking. Photo by Alex Davidson/Getty Images.
9. Jack Harrison
3 - Threatened to spark into life in the second half after a dreadful first half but then overplayed and ran into trouble. Photo by GLYN KIRK/AFP via Getty Images.
10. Tyler Roberts
3 - A couple of nice turns aside wasn't able to give Leeds forward momentum or impact the game. Photo by GLYN KIRK/AFP via Getty Images.
11. Rodrigo
2 - Completely ineffective. Offered next to nothing, took heavy touches or picked wrong options. No focal point for Leeds' attack. Photo by George Wood/Getty Images.
12. Adam Forshaw (sub)
5 - Tried to get on the ball, inject urgency and get Leeds playing but it didn't work. Wasn't always accurate, had few options at times. Photo by Catherine Ivill/Getty Images.